UNIFIED FUNCTIONAL METHOD FOR SOLVING GENERAL POLYNOMIAL EQUATIONS OF DEGREE LESS THAN FIVE
Dozie Felix Nwosu1*, Odilichukwu Christian Okoli2, Amaka Ezeonyebuchi3 and Ababu Teklemariam Tiruneh4
1Department of Mathematics/Statistics, Federal Polytechnic Nekede, Owerri, Imo State, Nigeria
2,3Department of Mathematics, Chukwuemeka Odumegwu Ojukwu University, Anambra State, Nigeria
4Department of Environmental Health Science, University of Eswatini, Mbabane, Eswatini
Considering the fact that the solution of solvable polynomial equations depends on the coefficients of the depressed equation which in turn depends on the coefficients of the standard polynomial equation, there is need to develop a unified method for solving ∑_(k=0)^n▒〖a_k x^k 〗=0;a_n≠0;n that incorporate a computational formula that relate the coefficients of the depressed equation and the coefficients of the standard polynomial equation, with the aim of ensuring that this method is valid for all n>5. We shall apply the undetermined parameter method of auxiliary function to obtain solutions to this polynomial equations of degree less than five in one variable. In particular, the result of our work is a unification and improvement on the work of several authors in the sense that their methods collapse (not valid) for the case of polynomial equation of degree one. Finally, our results improve and generalize the result recently announce in the literature. Beyond establishing the existence of these standard formula methods for solving higher degree polynomials, we are calling and as well recommending that effort should be made toward providing other variant methods that are simpler and friendly.
Keywords: Auxiliary Function, Cubic Equation, Linear Equation, Quadratic Equation, Resolvent Equation, Seeking Solution.
Published On: 30 September 2021